Conventional semiconductor modules comprise a baseplate on which one or more power semiconductor chips are arranged. To cool the power semiconductor chips, the power semiconductor module's baseplate is pressed against a heat sink. To improve the transfer of heat, a thermally conductive material, for example a thermally conductive paste, may be introduced between the baseplate and the heat sink in order to compensate for irregularities in the baseplate and the heat sink. However, the thermal conductivity of such thermally conductive materials is much lower than the thermal conductivity of both the heat sink and the baseplate. In principle, therefore, optimum cooling of the power semiconductor chips involved is desired for such arrangements. At the same time, it needs to be possible to fabricate such power semiconductor modules easily and efficiently. This also includes the possibility of making electrical contact with the power semiconductor chips on their top sides facing away from the heat sink using one or more bonding wires. In order to avoid short-circuits and/or a damage of the bonding wires, a deformation of the bonding wires after bonding them to the respective electrical connection partners shall be avoided.